{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Chapter 4 – Training Models**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This notebook contains all the sample code and solutions to the exercises in chapter 4._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "  <td>\n",
    "    <a href=\"https://colab.research.google.com/github/ageron/handson-ml3/blob/main/04_training_linear_models.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://kaggle.com/kernels/welcome?src=https://github.com/ageron/handson-ml3/blob/main/04_training_linear_models.ipynb\"><img src=\"https://kaggle.com/static/images/open-in-kaggle.svg\" /></a>\n",
    "  </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This project requires Python 3.7 or above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "assert sys.version_info >= (3, 7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It also requires Scikit-Learn ≥ 1.0.1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from packaging import version\n",
    "import sklearn\n",
    "\n",
    "assert version.parse(sklearn.__version__) >= version.parse(\"1.0.1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we did in previous chapters, let's define the default font sizes to make the figures prettier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rc('font', size=14)\n",
    "plt.rc('axes', labelsize=14, titlesize=14)\n",
    "plt.rc('legend', fontsize=14)\n",
    "plt.rc('xtick', labelsize=10)\n",
    "plt.rc('ytick', labelsize=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let's create the `images/training_linear_models` folder (if it doesn't already exist), and define the `save_fig()` function which is used through this notebook to save the figures in high-res for the book:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pathlib import Path\n",
    "\n",
    "IMAGES_PATH = Path() / \"images\" / \"training_linear_models\"\n",
    "IMAGES_PATH.mkdir(parents=True, exist_ok=True)\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
    "    path = IMAGES_PATH / f\"{fig_id}.{fig_extension}\"\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format=fig_extension, dpi=resolution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Normal Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.random.seed(42)  # to make this code example reproducible\n",
    "m = 100  # number of instances\n",
    "X = 2 * np.random.rand(m, 1)  # column vector\n",
    "y = 4 + 3 * X + np.random.randn(m, 1)  # column vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – generates and saves Figure 4–1\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.grid()\n",
    "save_fig(\"generated_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import add_dummy_feature\n",
    "\n",
    "X_b = add_dummy_feature(X)  # add x0 = 1 to each instance\n",
    "theta_best = np.linalg.inv(X_b.T @ X_b) @ X_b.T @ y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = add_dummy_feature(X_new)  # add x0 = 1 to each instance\n",
    "y_predict = X_new_b @ theta_best\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize=(6, 4))  # extra code – not needed, just formatting\n",
    "plt.plot(X_new, y_predict, \"r-\", label=\"Predictions\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "\n",
    "# extra code – beautifies and saves Figure 4–2\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.grid()\n",
    "plt.legend(loc=\"upper left\")\n",
    "save_fig(\"linear_model_predictions_plot\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.21509616]), array([[2.77011339]]))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `LinearRegression` class is based on the `scipy.linalg.lstsq()` function (the name stands for \"least squares\"), which you could call directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n",
    "theta_best_svd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function computes $\\mathbf{X}^+\\mathbf{y}$, where $\\mathbf{X}^{+}$ is the _pseudoinverse_ of $\\mathbf{X}$ (specifically the Moore-Penrose inverse). You can use `np.linalg.pinv()` to compute the pseudoinverse directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.pinv(X_b) @ y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradient Descent\n",
    "## Batch Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "eta = 0.1  # learning rate\n",
    "n_epochs = 1000\n",
    "m = len(X_b)  # number of instances\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1)  # randomly initialized model parameters\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    gradients = 2 / m * X_b.T @ (X_b @ theta - y)\n",
    "    theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trained model parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – generates and saves Figure 4–8\n",
    "\n",
    "import matplotlib as mpl\n",
    "\n",
    "def plot_gradient_descent(theta, eta):\n",
    "    m = len(X_b)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    n_epochs = 1000\n",
    "    n_shown = 20\n",
    "    theta_path = []\n",
    "    for epoch in range(n_epochs):\n",
    "        if epoch < n_shown:\n",
    "            y_predict = X_new_b @ theta\n",
    "            color = mpl.colors.rgb2hex(plt.cm.OrRd(epoch / n_shown + 0.15))\n",
    "            plt.plot(X_new, y_predict, linestyle=\"solid\", color=color)\n",
    "        gradients = 2 / m * X_b.T @ (X_b @ theta - y)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path.append(theta)\n",
    "    plt.xlabel(\"$x_1$\")\n",
    "    plt.axis([0, 2, 0, 15])\n",
    "    plt.grid()\n",
    "    plt.title(fr\"$\\eta = {eta}$\")\n",
    "    return theta_path\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1)  # random initialization\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.subplot(131)\n",
    "plot_gradient_descent(theta, eta=0.02)\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.subplot(132)\n",
    "theta_path_bgd = plot_gradient_descent(theta, eta=0.1)\n",
    "plt.gca().axes.yaxis.set_ticklabels([])\n",
    "plt.subplot(133)\n",
    "plt.gca().axes.yaxis.set_ticklabels([])\n",
    "plot_gradient_descent(theta, eta=0.5)\n",
    "save_fig(\"gradient_descent_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stochastic Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_sgd = []  # extra code – we need to store the path of theta in the\n",
    "                     #              parameter space to plot the next figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 50\n",
    "t0, t1 = 5, 50  # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1)  # random initialization\n",
    "\n",
    "n_shown = 20  # extra code – just needed to generate the figure below\n",
    "plt.figure(figsize=(6, 4))  # extra code – not needed, just formatting\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for iteration in range(m):\n",
    "\n",
    "        # extra code – these 4 lines are used to generate the figure\n",
    "        if epoch == 0 and iteration < n_shown:\n",
    "            y_predict = X_new_b @ theta\n",
    "            color = mpl.colors.rgb2hex(plt.cm.OrRd(iteration / n_shown + 0.15))\n",
    "            plt.plot(X_new, y_predict, color=color)\n",
    "\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index : random_index + 1]\n",
    "        yi = y[random_index : random_index + 1]\n",
    "        gradients = 2 * xi.T @ (xi @ theta - yi)  # for SGD, do not divide by m\n",
    "        eta = learning_schedule(epoch * m + iteration)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_sgd.append(theta)  # extra code – to generate the figure\n",
    "\n",
    "# extra code – this section beautifies and saves Figure 4–10\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.grid()\n",
    "save_fig(\"sgd_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21076011],\n",
       "       [2.74856079]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1000, tol=1e-5, penalty=None, eta0=0.01,\n",
    "                       n_iter_no_change=100, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())  # y.ravel() because fit() expects 1D targets\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.21278812]), array([2.77270267]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mini-batch gradient descent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code in this section is used to generate the next figure, it is not in the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–11\n",
    "\n",
    "from math import ceil\n",
    "\n",
    "n_epochs = 50\n",
    "minibatch_size = 20\n",
    "n_batches_per_epoch = ceil(m / minibatch_size)\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1)  # random initialization\n",
    "\n",
    "t0, t1 = 200, 1000  # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "theta_path_mgd = []\n",
    "for epoch in range(n_epochs):\n",
    "    shuffled_indices = np.random.permutation(m)\n",
    "    X_b_shuffled = X_b[shuffled_indices]\n",
    "    y_shuffled = y[shuffled_indices]\n",
    "    for iteration in range(0, n_batches_per_epoch):\n",
    "        idx = iteration * minibatch_size\n",
    "        xi = X_b_shuffled[idx : idx + minibatch_size]\n",
    "        yi = y_shuffled[idx : idx + minibatch_size]\n",
    "        gradients = 2 / minibatch_size * xi.T @ (xi @ theta - yi)\n",
    "        eta = learning_schedule(iteration)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_mgd.append(theta)\n",
    "\n",
    "theta_path_bgd = np.array(theta_path_bgd)\n",
    "theta_path_sgd = np.array(theta_path_sgd)\n",
    "theta_path_mgd = np.array(theta_path_mgd)\n",
    "\n",
    "plt.figure(figsize=(7, 4))\n",
    "plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], \"r-s\", linewidth=1,\n",
    "         label=\"Stochastic\")\n",
    "plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], \"g-+\", linewidth=2,\n",
    "         label=\"Mini-batch\")\n",
    "plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], \"b-o\", linewidth=3,\n",
    "         label=\"Batch\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(r\"$\\theta_0$\")\n",
    "plt.ylabel(r\"$\\theta_1$   \", rotation=0)\n",
    "plt.axis([2.6, 4.6, 2.3, 3.4])\n",
    "plt.grid()\n",
    "save_fig(\"gradient_descent_paths_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X ** 2 + X + 2 + np.random.randn(m, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–12\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "plt.grid()\n",
    "save_fig(\"quadratic_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly = poly_features.fit_transform(X)\n",
    "X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929,  0.56664654])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KNY89Rtzab0iPr8dPI6azsF9EqZvNStv/5AsNQEopFUrmzYOnn4bISKLnvMu9Xf9S5l2WNVlqYbQJTimlQsWWLTB0qP15wgTo2tXb8hRDA5BSSoWCY8fgmmvgjz/sstqjR3tdomJpAFJKqVDw8MOwbBk0aGBTW0cE/uU98EuolFKqaHPmwHPPQbly8N57UKOG1yXyiQYgpZQKZj/9BDfeaH9++mn3ljP1Aw1ASikVrNLS4Ior4MABe3/vvV6XqEQ0ACmlVDASgZEj4fvv4cwzYdq0UuV585IGIKWUCkZTp55c32f2bIiL87pEJaYBSCmlgs2KFXDHHfbnf/4TWrXytjylpAFIKaWCyd69cOWVdt7P7bfDDTd4XaJS0wCklFLB4vhxGDzYZjzo1Amef97rEpWJBiCllAoWY8fCl19CfDx8+CFER3tdojLRAKSUUsFg7lyb3y0iwk42rV/f6xKVmQYgpZQKdKmpJ/t6Jk+Gnj29LY+faABSSqlAtn8/XH45HDxok42OGuV1ifxGA5BSSgWqrCy4/nr48Uc71Hrq1KCbbFoUDUBKKRWoxo+HTz6BatXgo4+gYkVXD5+cDJMm2Xsn6IqoSinlZ8nJdgnruLg4evQo5U7mzoUnnrCDDt55B844w38F9EFyMlxwgZ1uVL68XZbb33lONQAppZQf5b5wlyvXhvbtS3HhXrfONr0BTJwIF13k93IWJynJnsPx4/Y+Kcn/AUib4JRSyo9yX7gzMgxJSSXcwe+/w2WXwaFDdtLpgw+esonTTWMAPXrYmk9kpL0vdU2uCFoDUkopP8q5cNsakJTswp2ZaUe6/fortG8Pb755yqADN5rGwO5z0SIbUHv0cOYYGoCUUsqPcl+44+LWkJDQ3vcXjxplX1yzpu0Diok5ZRM3msZyJCQ4u76dBiCllPKznAt3UtIB31/0xhvw4osQFWWXV2jQoMDNctewnGoac4sGIKWU8tpXX9nF5cAur9C1a6GbutE05hYNQEop5aVNm+xy2pmZcP/9MHx4sS9xumnMLToKTimlvHLgAPTvb0e+XXwxPP201yVylQYgpZTyQmYmXHstbNgALVrYyaaRkV6XylUagJRSygv33w+ffw41ath0O1WqeF0i12kAUkopt738Mrz0kh3GNneu62l2AoUGIKWUctP8+XD33fbnN98scsRbqNMApJRSblm3zmY6yMqCRx89me8tTGkAUkopN+zYAZdcYke+XXWVXWohFzfyuwUaV+YBGWOqAm8CLQEBhotIGL3NSqmwduiQHW69daudwDNjhl1mIZtb+d0CjVs1oH8A80WkOdAGSHXpuEqpEBG0NYTjx2HQIPjuOzvY4D//OSXHW0H53cKB4zUgY0wc0A0YBiAix4BjTh9XKRU6ArmGkLP4XIFpcUTgnntg3jyoXh0++wzi40/ZRyjldysJIyLOHsCYtsDrwAZs7WcVcI+IHM61zQhgBEB8fHyH999/39EyBaJDhw5RqVIlr4vhqnA8Z9DzLo1ZsxoybdppZGUZIiKyGD58M0OGbPFzCUtu/fo4Ro1qQ0ZGBFFRWTz77BrOPvtkAtKaM2dy1r/+RVZUFGueeYb9rVsXua+UlKq0bbsvzz6CUc+ePVeJSMdiNxQRR29ARyAT6JT9+B/Ak4Vt37RpUwlHiYmJXhfBdeF4ziJ63qWxdKlITIxIZKS9X7rUf+Uqi4kTbZnA3k+cmOuX77xjfwEi777rWRm9AKwUH+KDG4MQtgHbRGR59uMPgTEuHFcpFSICNQN0oU1nSUkwdKj9+Zln7NBrdQrHA5CI7DLGbDXGNBORjcAF2OY4pZTyWSBmgC4wMK5fD5dfDseOsW3gQOrff7+3hQxgbi3HcBcwyxhTHtgE3OjScZVSylF5AuPWrdC3L+zfDwMH8vPIkdTPt6S2OsmVACQiKdi+IKWUCk1//AEXXQTbttn0Om+9BcuXF/+6MKaZEJRSykeFzkVKS7MTTVNT4eyz4eOPT5nro06lK6IqpZQPCp2LlLOuz9Kl0KCBTTZarZrXxQ0KWgNSSikfFJitQARuucWu51O9OnzxBdSv73FJg4dPAcgYs80Yc3++51oZY44aY85ypmhKKRU4coZcR0ZCuXKw5Tdhx5DRMH06xMbabActWnhdzKDiaw0oGTgn33MvAG+KiA6pVkp5xq0ccTlDrm+5xVZ8qr0+mbrvPEtWuSiYM+eUMeLJyTaDQ9DlrnORr31AycDInAfGmMuBdsDVDpRJKaV84naOuIQE2/Q2LOMNJsrDZGH4+Mp/c/lFFxVYrvT005g1K7By1wUSX2tAy4AzjDHVjTHRwDPAeBH53bmiKaVU0bzIIn3F8fd5RW4D4L6ol6l196lZDnLKlZVlwiq7dUn5GoBWYTNYdwTuxeZ2e9mhMimllE9y98u4kkX6s89o+sQQIsniqz5/59qvbi+wZpNTroiIrLDKbl1SPjXBiUi6MWY10B8YCgwWkQxHS6aUUsVwNUfcV1/BFVfYYdejR9N98iNQSJKDnHJNm7aZ4cNP1+a3QpRkHlAycA/wpYjMc6g8SilVIq7kiFuxAi69FI4ehdtug8mToZgUOwkJkJ6+hYSE0x0uXPAqyTygFCAL0Mx6SqnwsWaNTbFz6BAMHgwvv1xs8FG+KUkAGgK8JiLrnSqMUkoFlA0boHdv+PNPGDDAzvmJ0Pn7/lJkE5wxJgKIxy6n3QrQRS2UUuHhp5/sWOq9e22G6/feg6gor0sVUorrA+oGLAY2AleIyJ/OF0kppTz266/Qqxfs2mXv58yB6GivSxVyigxAIpKE5otTSoWTzZuhZ0+7rEKXLprZ2kEaXIrgVooPpVSA2LLFBp/ffoNOneCzz6BiRa9LFbJ0OYZCuJ3iQynlsa1b7WSizZvh3HNtZuu4OK9LFdK0BlQIL1J8KKU8sm2brfn8+it07GiDT5UqXpcq5GkAKoTrKT6UUt7YsgW6d4dffoH27WHBAqha1etShQVtgiuEqyk+lFLeyBlwsHkzdOgAX36pq5m6SANQEVxJ8aFUAElODqMvXZs22eCzZcvJPp+qVcPrPfCYBiClFBBmA29yJplu3QrnnQfz50OVKuH1HgQA7QNSSgHBO/CmxNMlNmyAbt1s8OncOc+Ag2B9D4KV1oCUUsDJgTc53/6DYeBNiWssKSnQp49Nr9Ozp51kWqnSiV8H43sQzDQAKaWA4Bx4U1CNpdByf/stmb0votzBffx5Xl+qfTrnlAwHwfgeBDMNQEqpE4Jt4I3PNZbERI5fehnl0g4xl8sZlvIun6dEF3iuwfYeBDMNQEqpoJVTY5k5s4iNPvkErrqKyPR03jGDuEFmIBlReWpLOvLNGxqAlFJBb8YMWwuaMSNfP9Dbb8MNN8Dx4+z6623c/PnLSEZEntqSjnzzjo6CU0oFtUJHrr3yClx3nf3FmDHUnv0KCxdH8OSTeYOMjnzzTljUgLR6rVToOqUfqLvAuCfgiSfsBpMmwZgxQMH9OzryzTshH4C0eq1U8PLly2OekWvnHydh1t229hMRAa+9BjffXOz+X3gBfv9dv6S6LegDUHEf0BIN01RKBYySfHlMSICE9um2v+f99+3qpe++C5df7pf9K2cEVQDKH2x8+QBp9Vqp4FSiL4/79sFf/2o3iouzE0y7d/ff/pUjgiYAFRRsfPkA6cQypYKTz18et22Diy+GdeugTh27imnbtv7bv3KMKwHIGBMJrAS2i8ilpdlHQcHG1w9QME8s0wEUKlz59OVx/Xro29cGoebNbVLRRo38t3/lKLdqQPcAqUCx69tG7dsHImBMnucLCjah/gHSNmoV7or88rh4MQwcCPv3Q5cuttmtenVXy6fKxvEAZIypD/QDJgD3F7d9hT174JZb4NVXISrqxPOFBZtgrt0UR9uolSrEjBl2dFtmpu37mTXrlLxuxdEveN5zYyLqC8CDQJZPWxsDU6fya4uL+XbBvjy/SkiAhx8Onw+JLguuVD4i8PjjMGyYDT6jRsEHH5Q4+IBOQA0ERkSc27kxlwKXiMhIY0wP4IGC+oCMMSOAEQC1K9fskHIQarGHVNOCFWMn07B7ZcfKGCgOHTpEpVxp4XOsXx9HSkpV2rbdx9lnH/CgZM4p7JxDnZ536UQcO0azKVOotXAhEhHBT3fdxY4ihlkXZ/36OEaNakNGhiEqSnj22TV+/x8L1791z549V4lIx2I3FBHHbsAkYBuwGdgFpAFvFfWav/ylpZwe8aus4ywRkEMV40W++UZCXWJiotdFcF04nrOInnep7NolkpAgAiIVK4rMm+eXMi1dKjJxor13Qrj+rYGV4kOMcLQJTkQeFpH6ItIYuBZYLCLXFfWamJjj7IxuzPkRS1kY0YeKh/9nF44qMt2tUipkff89nHuu7bRp0AC++Qb69fPLrsOtWT/QBFwy0piY4yxaBKP/XoWKSZ/BnXfaBtqhQ20+pyzfupKUUiHgk0/sstlbtkCnTvDtt9CmjdelUn7i2kRUEUkCknzZ9uTItnJw/ktw1llw110weTKkpsK//21nOyulQpOITSL62GP252uvhWnTSjXYoDg61847wZEJ4fbb4cwz4aqr7Fj/886D//zHPqeUCi1paTB8OLz3nh0VO2GCbSfLNzfQH3QotrcCrgmuUL17w4oVtjaUmmrbhOfP97pUSil/+u036NrVBp/Kle0XzUcecST4gA7F9lrwBCCAJk1g2TKb4XbfPtsR+dRTtoquVBhITrYtU8nJXpfEAQsXQocOsHo1nHGG/V/v39/RQ+pcO28FVwAC+61o9mwYO9YOSHj4YbjiCjgQWnNklMovp7nob3+z96EQhJKTYdJE4bc7p8BFF9lFeS6++GRrB84G3ZwMK/lXSVXuCI4+oHySl0eQFD2Ov05uT/MJ18NHH8GGDTBnzokPrVKhxsvUTE501Ccnw4BeB3k5/SYayQf2ycceg3HjbJUEd/poQjmdV6ALugCU+wP5ZPnL+Gb6Sto9OdCmYu/UCd54w46YKeS1OtpFBSuvlg9wKgise289/z16Bc3ZyAEqs+C6mVz55OV5ttF8iKEt6Jrg8n8g5/9ypm0rHjQIDh2CQYPYdcUdPP1kep4qeyg2X6jw4lVzkSMd9W+9xfDXzqU5G1lLK7pGr6TeyMtP2Uz7aEJb0AWgAj+QFSvabLgvv0xWVHlqz3mFno935caem08EGh3tokKBFzP3/RoEjhyBW2+F668n8mgaey6+gS/GLeO1xKYFnpP20YS2oGuCK3QNIGNg5EhmrD+XHq9cxTmsJDm9HYv/byokDNTVD5UqJX+tuxW7ZQvcfbdNrRMdDS++SM1bbmF0MUOstY8mdAVdAIKiP5DNr+tIl2nf8c+jw7iMj7ni7Sug6kgSnn2WRYsqaB+QUqVQ5iAwcyYdbr0Vjh6Fpk3tPB8fls1WoS3omuCKk5AAsxdXY/2Eufx6zwt2UbtXXoFOnUio9kOZmi9Ceg6GUk44cABuuAGGDiXy6FEYMgRWrtTgo4AgrQEVx35bM8A9cH1XOypu7Vpo3x6efx5GjCjxzGpN2aHChd9Giy5fDoMHw6ZNEBvLD3fcQfPJkx3LaqCCT8jVgE7RoQN89x1cf73tAL3tNruE7969JdpNYYMYtFakQolfRosePw4TJ0KXLjb4tGsHq1ax65JLNPioPEI/AIHNnjBzJrz9NlSpYvNLtW4NX3zh8y4KGgmkQ7tVqCnzaNFNm6B7d3j0UbuTUaPsP0bz5g6UVgW78AhA2ZIbD+LlEWs40KYr7NwJffvCyJFw+HCxry1oOKgO7S45rTEGtlIPuRaBN9+0X+y++Qbq1LFf8J55xo54U6oAIdkHVJCTfTiNeCgqifW3TaHR1Mfh1VdhwQJbQ+rcuch95B8JpEO7SyZ/P9qUKXH6ngWYUg253rnTzu355BP7+Oqr7f9V9eoOllSFgrCpAeWurRzNiOTthmP48KEVbKrUCn75Bc4/H0aPtv1EPtJJciWTv8aYklLV6yKpAvg82VXETgA/+2wbfKpUsY/ffVeDj/JJ2ASg/E0L+/bBVX9vQ4tDK3iKh8gSbHNBu3Ylah/SNeULVlBTW/6/Qdu2+7wqXlALiGbMXbtg4EC47jr480/bnL1unR31pgMNlI/Cpgkuf9PCuHH2+WNE8zBPseOcv/LiwRvtYnddusC999qqTcWKnpU5WJOnFjZkPf/fID1dl9AoKc+nA4jAjBlw//028FSubKc2DB+ugUeVWNjUgCBvbeWKK/L+ruVNnexw7TFj7D/S889Dy5a2f8gDwTzCrqjBGVpjLBtPB778+qtds+fGG23wuegiW+u56SYNPqpUwioA5TZiBLz2Glx4ob0fMQKoUMG2bSxfDm3awObN9p9s6NASzxsqq2AeYacZjJ3jyXubkWGbp1u2hC+/tP07M2fC559Dw4YuFECFqrANQGCDzhdfZAef3Dp2tCsyTppkh5DOnGnnMUybZldhdUEwX8R1cIZzXH9vly2z/w+jR0Namh3hlppqJ3ZrrUeVUdj0AZVYVJRtjrviCps9YfFi29QwbZodYtqqlaOH91cGYq9oBmPnuPLe/vGHnUz62mu236dxY3j5ZbjkEocPrMJJWNeAfHLmmbBwIbz1FtSsaSfZtW9vO2H373f00NpfolyXlWUnlDZrBv/8p62CP/QQrF+vwUf5nQYgXxhjs/j+8APcfrvtmHn+eftPOnOma81ySjlq5Uo7GfuWW2yfZ7dusHo1PPUUxMZ6XToVgjQAlUS1anZph5UrbbVk9247QKFrV/j2W69Lp5TP8swl2rEDhg2Dc86xA3Dq1LF5E5OS7MADfx1HqXy0D6g02reHr7+2zXIPPmj/uzp1srWkSZOgQQOvS6hUoXKG+EekH+FoxPOcGzWRyCOHbb/nvffasf+VK/vtOJp6SRVGa0ClFRFhF9r68Uc7WCE62qYhadbM/gMfOFDotz/9Vqi8lLQ4i6uPzmRDVjOeyHzUBp8BA2DDBnj6ab8EH9DUS6p4GoDKKi7ORpPUVDtE9cgR+PvfyWjUhA+6v8T4x47lmUgayBNMNTCGgYULuXtGB6bLUBqylbWmNetfXAhz50KTJn49lKZeUsXRAOQvp51m17n/5hvo0oWoff/juYy7WZfVgoFH3yZpsR2oEKgTTAM5MCo/WL4ceveGPn2o+FMK6TXrM+/K6Rz+73ecfdcFpdplcV9Y8s9ZOvtsTb2k8tI+IH/r3BmWLOGHpz+Gh8fQXH7gLRlC2rRJcNZ4enS/nPLlTamXcHAqP1xBgdHfw7+DNbddUFu3Dh57zC7CCDZj9UMPEX3vvVwaE1Pq3fqaky73nKVA+bKlAocGoDIq8KJqDM0fGkBy5358+sIMen8znthN62DgQBI6dmTV+LHMPdaPHj1NiS7ERf3Tl/Xi7vTaRgWVPZQEXHBdvx7Gj4cPPrATSWNj4Z57bEaDatXKvHs3vrCo0KcBqAyK+xaYcH45OP8mSL8O3ngDJkyAlStpsbI/LTp0gJaPg/T3OaVJYf/0/siQ7HTmhVC+YHmeoTq3detsm1dO4Clf3uaaevRRqF3bb4fRxRiVP2gfUBn43J8THQ133mkXvnvuOXshWLXKjjxq1w7efZcNa2OLHQBQWH44f/UrOZl5IZhz2xUnIPr1li+Hyy+3KaLef98Oqb7jDvuZe+klvwYf0Hx/yj+0BlQGJf4WGBsL991nc8u98QZMngxr1sCgQfTldJ4xo7kkehifLa5QaHt6QbWUYPg2WlDZQ6VPwLP3X8Rmp3766ZNtmhUqwM032/Q59es7enjN96fKTEQcvQENgEQgFVgP3FPU9k2bNpWyWLpUZOJEe++GMh3vyBGR116TP6qfIWIvJ7KbePnvBeNEdu92rxweSUxM9LoIflOS97+o8/ZpP+npItOni7RqdeJzI5Uri4wZI7JrV4nL7pZQ+nv7KhzPWUQEWCm+xAdfNirLDagDtM/+uTLwI3BWYduXJQAtXSoSEyMSGWnvg+VivHRJpgwu946spP3JC0p0tMjNN4usXet18RwTrv+chZ13sZ/fXbtExo8XqVPn5OekTh2RSZNE/vzT6WKXWTj+vcPxnEV8D0CO9wGJyE4R+S7754PZNaF6ThwrINriSyGhaySdX2jKggkrWf9yElx2mT2BN9+E1q050K677VTOyPC6qCGpoPksXkzKLfDzK2LzDN5wg1387fHHYedOm6Nt+nS7aOKYMVC1aqmPqxOQlVdc7QMyxjQG2gHLndh/MPSFFObssw/Qo4cBusPI7qx+70eWDXmJ645PJy7lv3D1f22SyJtusrfGjb0uckgobHi4F6Pacn9+q0cd5Op9b0OH12xGarCjJQcMgLvugl69/LIgXECN4FNhx9jakgsHMqYS8BUwQUTm5PvdCGAEQHx8fIf333+/1MdZvz6OlJSqtG27L6hmXh86dIhKlSqdeDxrVkOmTTuNilkHucHM5JEq/6Duvp8BEGP4s2NHdvbrx96EBKR8ea+KXSb5z9kLOe9zVpYhIiKL4cM3A5zy3JAhW/x2zELPW4Tf520m/tP5nLd5HuXT0wDIiItj58UXs+Oyyzhat67fygEFn78/zzW3QPh7uy0czxmgZ8+eq0SkY7Eb+tJOV9YbEAV8Adxf3LZlHYQQDArqaM7fVnxKf8A3WSJffSUyZIjtH8rpA6hWTWTkSJHly0Wystw9kTIKhPbxgvpdnO5LPOW8t2yx/TjNmp38u4Lsb3O+yKxZdrCKQ9zsNw2Ev7fbwvGcRXzvA3K8Cc4YY4CpQKqIPOf08QJdSVKY5B22bIBudpGwF1+Ef//b9gGkpNg1il55BZo2hUGD7K1ZM1fPyylOZxgobGi748uh//EHfPihzaD+3/+eePpYjdq8tP8G/pU1jE0/tmDRaZBQwYHjZwv2pd9VkPMlSpXlBnQFBFgLpGTfLils+1CvAU2caL9tgr2fONE+X+pvSikpIvfdJ1KzZp5vz9Kund35xo1+K7u/h3oXd87BOqqxUL//LjJ1quw991yRcuVO/q0qVBC56iqRefNk0pMZBX4+QkE41gbC8ZxFAqgGJCJfA2XvLQ0Rfh8o0aaNza7w9NOweLFdyfKjj2zH9erV8MgjdsTUwIF2dF27dnYtoxLyorM6JNL3/PYbfPIJfPwxJCZCZiY1wP4Neve2ixgOHGiX9QC6V4fyE4NzII1SJaWZEFzmWJNHuXJw4YX29s9/wvz5MHu2vfitW2dv48dD3brQr5+99ex54sJXHC+CQVCOaszMhGXL4PPP4bPPbBNpjshI6N2bja1b02zMGIiPP+XlZfl8BFxCVKWKoQGolMryz+54CpMKFWxesMsvt1fvxYttOv5PPoHt220aoDfesEErIQEuushWbzp0sDnECuBFMCjqYhwwF1sRuyru4sW2sAsXwv79J39fsaJ9fwcMsEG/Rg12JiXRrIDgk6M0nw8dTq2CkQagUgiqf/by5aFvX3t75RX7jXzePFtDWr4cliyxt8cesxfLrl2he3d737EjZK8Z4+s3c38HhoIuxp6+/1lZdqmDb76x71tSEuzYkXebZs1Ovuc9etgvBA4LieZKFXY0AOXjywU0aP/ZjbF9QO3a2aVP9+2z39wXLLAnsXEjfPGFvYGtDbVvD+edB+ecQ0LHjiQ8dOaJPqT875VbgcHV93/3blixwmYj+PZbG7T37cu7TXy8nRjasyf06QOnn+5QYQoXlM2VKuxpAMrF1wuo1//sfqtlVK1qO8AHDrSPd+6Er76yt6VL4fvv7QV3ea7EFZUrQ5s27KrZmrc/aU3K8Va8VL4FsxdXcy0wOPL+Hzlim9I2bIC1a21Ncc0a+57k17ChrSF26QLnn28HefghK0FZ6HBqFYw0AOXi6wXUy392R2sZderAtdfaG8CBA7ZD/dtv7fpFK1fCtm3w9dfU5mteynndUTjcpyZnN2lGbZrxszmdrRGncWn8abCrEdSsWaqRd4Up1fsvYmsuW7fakWm//HLytnEj/Pqr3Sa/SpVsU+S55568NWjgt3PxJ10eQQUbDUC5lOSbtVf/7K42P8XFnRxZl2PXLli7ls2ffM/Xr67lrOPf04yNVDy8B9bs4UaW2O0ygFuyX1OunA1u9epBrVq2ySo+nvr798OmTVClij1W5cq2z6lCBXsrX94Grpzb8eN2lFlmJgk1M0i4NA3S0iAxDQ4dgj//tEHmzz/hf/+DPXtsE9ru3TZwHj5c+LlGRkKTJtCihV3UrW1bO8T9tNP8GjyVUidpAMolGJoxvG7+o3ZtqF2bxhdeyM7B8EUSpHfLIqHhdluT+PFHW5v49VcbXLZuhb177f3WrXl21cTlolOpkq29NGwIZ5xx8nbmmTb4BGlOPaWClQagfAK9GSOQguTJ9yoCaGAv7r17n7rh0aN2pNj27bZmkn3blpJC/cqVbVPf/v1w8KDd9sgRe8vMtKPOsm8ZWZEcPV6O8rHliI4tZ1eYzblVqgTVqtl+rapVbS2rZk1b46pVy9a+qlQp8ny8GtodMEPKlXKZBqAg5GaQ9MvFsUIFOzIs3+iwn5OSqO9jFS5P31cmLPrIv++BV0O7g2pIv1J+po3bqlA5F8e//c3ee7lgmdOLDXq1mKHXiyjqYnTKS1oDUoUKpPlOTvd9Ob3/3DVJN49bXJm09qW8pAFIFcrzAQ+5ON335eT+81/op0yJO/FeetmnF0hfMFR40gCkChVIAx5yyuNkGZzaf/4LfUpKVVeOW5xA+oKhwpMGIFWkQB8VGAzyX+jbtt3ndZGAwPuCocKPBiClHJb/Qp+efsDrIp2gXzCUlzQAKeWC3Bd6t0e6KRWodBi2UkopT2gAUkop5QltglN+pWllClbYPKBAoH8z5RUNQMpvvJ7YGKgX0qLmAXnN67+ZCm/aBKf8xsu0MoGUNii/4uYB5fAiLY7XqYBUeNMakPIbLyc2BvKsfl/mAXlVE9HJqMpLGoCU33g5sTGQL6S+zAPyKoDqZFTlJQ1ADgrUPgkneTWxMdAvpMXNA/IygOpkVOUVDUAOcbJJJRgCmxdlDOYLaaAHUKWcoAHIIU41qQTDqKVgKGMgCuYAqlRp6Cg4h+Q0qURG+rdJJRhGLQVDGZVS3tMakEOcalIJ5M72HMFQRqWU9zQAOciJJpVg6CsIhjKWVjD0vykVLDQABaFg6CsorozJyTBrVkOiowvfLtAu9tq3pZR/aQBSrsu5kKenn8asWQVfyAPxYh/Ik12VCkY6CEG5LudCnpVlCh2kEIgDGZwaWKJUuNIakHJdzoU8PT2L8uUjCryQB+JAhlDu21LKCxqAlOtyLuTTpm1m+PDTC7yQB+rFPhj635QKFq4EIGNMX+AfQCTwpog85cZxlbPKMkggIQHS07eQkHB6kdvoxV6p0OV4ADLGRAIvA32AbcAKY8zHIrLB6WMr5wTiIAGlVHBxYxDCucDPIrJJRI4B7wIDXDiuclAgDhJQSgUXIyLOHsCYK4G+InJz9uPrgU4icmeubUYAI7IftgTWOVqowPQXYK/XhfBd5YpwZlPAAAI//QgHD5dwJ0F2zn6j5x0+wvGcAZqJSOXiNnKjD8gU8FyeqCcirwOvAxhjVopIRxfKFVDC8bzD8ZxBz9vrcrgpHM8Z7Hn7sp0bTXDbgAa5HtcHdrhwXKWUUgHMjQC0AjjTGHOaMaY8cC3wsQvHVUopFcAcb4ITkUxjzJ3AF9hh2NNEZH0RL3nd6TIFqHA873A8Z9DzDifheM7g43k7PghBKaWUKojmglNKKeUJDUBKKaU8EZAByBjzpDFmrTEmxRizwBhT1+syucEYM8UY80P2uX9kjKnqdZmcZoy5yhiz3hiTZYwJ6eGqxpi+xpiNxpifjTFjvC6PW4wx04wxe4wxYTO/zxjTwBiTaIxJzf583+N1mZxmjKlgjPnWGLMm+5yfKPY1gdgHZIyJE5ED2T/fDZwlIrd5XCzHGWMuBBZnD9yYDCAiD3lcLEcZY1oAWcBrwAMi4tP8gWCTnZLqR3KlpAIGhUNKKmNMN+AQMFNEWnpdHjcYY+oAdUTkO2NMZWAVcHko/72NMQaoKCKHjDFRwNfAPSKyrLDXBGQNKCf4ZKtIvomroUpEFohIZvbDZdg5UyFNRFJFZKPX5XBB2KakEpH/An94XQ43ichOEfku++eDQCpQz9tSOUusQ9kPo7JvRV67AzIAARhjJhhjtgJDgMe9Lo8HhgOfe10I5Tf1gK25Hm8jxC9IyjLGNAbaAcs9LorjjDGRxpgUYA/wpYgUec6eBSBjzEJjzLoCbgMARORREWkAzALuLHpvwaO4887e5lEgE3vuQc+Xcw4DxaakUqHHGFMJmA3cm69lJySJyHERaYttvTnXGFNkk6tnC9KJSG8fN30b+BQY62BxXFPceRtjhgKXAhdIIHbQlUIJ/tahTFNShZnsfpDZwCwRmeN1edwkIvuMMUlAX4pILh2QTXDGmDNzPbwM+MGrsrgpe+G+h4DLRCTN6/Iov9KUVGEku0N+KpAqIs95XR43GGPic0buGmNigN4Uc+0O1FFws4Fm2NFRvwG3ich2b0vlPGPMz0A08Hv2U8tCffSfMeavwEtAPLAPSBGRizwtlEOMMZcAL3AyJdUEb0vkDmPMO0AP7NIEu4GxIjLV00I5zBjTFVgCfI+9jgE8IiKfeVcqZxljWgMzsJ/vCOB9ERlf5GsCMQAppZQKfQHZBKeUUir0aQBSSinlCQ1ASimlPKEBSCmllCc0ACmllPKEBiCllFKe0ACklEOyl5pIN8Y0yvXcP4wxvxhjanlZNqUCgc4DUsoh2bPhVwCrReQWY8wDwINAFxH5ydvSKeU9z3LBKRXqRESMMY8AnxpjfgEeBXrlBB9jzMfA+cAiEbnSw6Iq5QmtASnlMGPMUux6QP1F5PNcz/cEKgFDNQCpcKR9QEo5yBjTC2iDXY5hd+7fiUgicNCLcikVCDQAKeUQY0wbYA5wFzAXmORpgZQKMNoHpJQDske+fQY8JyLTjDHfAmuNMT1EJMnb0ikVGLQGpJSfGWOqA/OBeTnp6EVkHfABWgtS6gStASnlZyLyB9CigOev8aA4SgUsHQWnlEeMMQuxAxQqAn8AV4lIsrelUso9GoCUUkp5QvuAlFJKeUIDkFJKKU9oAFJKKeUJDUBKKaU8oQFIKaWUJzQAKaWU8oQGIKWUUp7QAKSUUsoTGoCUUkp54v8BTDN9Ocao1zcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–13\n",
    "\n",
    "X_new = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "X_new_poly = poly_features.transform(X_new)\n",
    "y_new = lin_reg.predict(X_new_poly)\n",
    "\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "plt.grid()\n",
    "save_fig(\"quadratic_predictions_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–14\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "plt.figure(figsize=(6, 4))\n",
    "\n",
    "for style, width, degree in ((\"r-+\", 2, 1), (\"b--\", 2, 2), (\"g-\", 1, 300)):\n",
    "    polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    std_scaler = StandardScaler()\n",
    "    lin_reg = LinearRegression()\n",
    "    polynomial_regression = make_pipeline(polybig_features, std_scaler, lin_reg)\n",
    "    polynomial_regression.fit(X, y)\n",
    "    y_newbig = polynomial_regression.predict(X_new)\n",
    "    label = f\"{degree} degree{'s' if degree > 1 else ''}\"\n",
    "    plt.plot(X_new, y_newbig, style, label=label, linewidth=width)\n",
    "\n",
    "plt.plot(X, y, \"b.\", linewidth=3)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "plt.grid()\n",
    "save_fig(\"high_degree_polynomials_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning Curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.model_selection import learning_curve\n",
    "\n",
    "train_sizes, train_scores, valid_scores = learning_curve(\n",
    "    LinearRegression(), X, y, train_sizes=np.linspace(0.01, 1.0, 40), cv=5,\n",
    "    scoring=\"neg_root_mean_squared_error\")\n",
    "train_errors = -train_scores.mean(axis=1)\n",
    "valid_errors = -valid_scores.mean(axis=1)\n",
    "\n",
    "plt.figure(figsize=(6, 4))  # extra code – not needed, just formatting\n",
    "plt.plot(train_sizes, train_errors, \"r-+\", linewidth=2, label=\"train\")\n",
    "plt.plot(train_sizes, valid_errors, \"b-\", linewidth=3, label=\"valid\")\n",
    "\n",
    "# extra code – beautifies and saves Figure 4–15\n",
    "plt.xlabel(\"Training set size\")\n",
    "plt.ylabel(\"RMSE\")\n",
    "plt.grid()\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.axis([0, 80, 0, 2.5])\n",
    "save_fig(\"underfitting_learning_curves_plot\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "polynomial_regression = make_pipeline(\n",
    "    PolynomialFeatures(degree=10, include_bias=False),\n",
    "    LinearRegression())\n",
    "\n",
    "train_sizes, train_scores, valid_scores = learning_curve(\n",
    "    polynomial_regression, X, y, train_sizes=np.linspace(0.01, 1.0, 40), cv=5,\n",
    "    scoring=\"neg_root_mean_squared_error\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – generates and saves Figure 4–16\n",
    "\n",
    "train_errors = -train_scores.mean(axis=1)\n",
    "valid_errors = -valid_scores.mean(axis=1)\n",
    "\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(train_sizes, train_errors, \"r-+\", linewidth=2, label=\"train\")\n",
    "plt.plot(train_sizes, valid_errors, \"b-\", linewidth=3, label=\"valid\")\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.xlabel(\"Training set size\")\n",
    "plt.ylabel(\"RMSE\")\n",
    "plt.grid()\n",
    "plt.axis([0, 80, 0, 2.5])\n",
    "save_fig(\"learning_curves_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularized Linear Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ridge Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's generate a very small and noisy linear dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# extra code – we've done this type of generation several times before\n",
    "np.random.seed(42)\n",
    "m = 20\n",
    "X = 3 * np.random.rand(m, 1)\n",
    "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n",
    "X_new = np.linspace(0, 3, 100).reshape(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – a quick peek at the dataset we just generated\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(X, y, \".\")\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$  \", rotation=0)\n",
    "plt.axis([0, 3, 0, 3.5])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.55325833]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "ridge_reg = Ridge(alpha=0.1, solver=\"cholesky\")\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x252 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–17\n",
    "\n",
    "def plot_model(model_class, polynomial, alphas, **model_kwargs):\n",
    "    plt.plot(X, y, \"b.\", linewidth=3)\n",
    "    for alpha, style in zip(alphas, (\"b:\", \"g--\", \"r-\")):\n",
    "        if alpha > 0:\n",
    "            model = model_class(alpha, **model_kwargs)\n",
    "        else:\n",
    "            model = LinearRegression()\n",
    "        if polynomial:\n",
    "            model = make_pipeline(\n",
    "                PolynomialFeatures(degree=10, include_bias=False),\n",
    "                StandardScaler(),\n",
    "                model)\n",
    "        model.fit(X, y)\n",
    "        y_new_regul = model.predict(X_new)\n",
    "        plt.plot(X_new, y_new_regul, style, linewidth=2,\n",
    "                 label=fr\"$\\alpha = {alpha}$\")\n",
    "    plt.legend(loc=\"upper left\")\n",
    "    plt.xlabel(\"$x_1$\")\n",
    "    plt.axis([0, 3, 0, 3.5])\n",
    "    plt.grid()\n",
    "\n",
    "plt.figure(figsize=(9, 3.5))\n",
    "plt.subplot(121)\n",
    "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n",
    "plt.ylabel(\"$y$  \", rotation=0)\n",
    "plt.subplot(122)\n",
    "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)\n",
    "plt.gca().axes.yaxis.set_ticklabels([])\n",
    "save_fig(\"ridge_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.55302613])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(penalty=\"l2\", alpha=0.1 / m, tol=None,\n",
    "                       max_iter=1000, eta0=0.01, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())  # y.ravel() because fit() expects 1D targets\n",
    "sgd_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.55321535]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# extra code – show that we get roughly the same solution as earlier when\n",
    "#              we use Stochastic Average GD (solver=\"sag\")\n",
    "ridge_reg = Ridge(alpha=0.1, solver=\"sag\", random_state=42)\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.97898394],\n",
       "       [0.3828496 ]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# extra code – shows the closed form solution of Ridge regression,\n",
    "#              compare with the next Ridge model's learned parameters below\n",
    "alpha = 0.1\n",
    "A = np.array([[0., 0.], [0., 1.]])\n",
    "X_b = np.c_[np.ones(m), X]\n",
    "np.linalg.inv(X_b.T @ X_b + alpha * A) @ X_b.T @ y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.97944909]), array([[0.38251084]]))"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_reg.intercept_, ridge_reg.coef_  # extra code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lasso Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.53788174])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "lasso_reg = Lasso(alpha=0.1)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x252 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–18\n",
    "plt.figure(figsize=(9, 3.5))\n",
    "plt.subplot(121)\n",
    "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n",
    "plt.ylabel(\"$y$  \", rotation=0)\n",
    "plt.subplot(122)\n",
    "plot_model(Lasso, polynomial=True, alphas=(0, 1e-2, 1), random_state=42)\n",
    "plt.gca().axes.yaxis.set_ticklabels([])\n",
    "save_fig(\"lasso_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 727.2x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this BIG cell generates and saves Figure 4–19\n",
    "\n",
    "t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n",
    "\n",
    "t1s = np.linspace(t1a, t1b, 500)\n",
    "t2s = np.linspace(t2a, t2b, 500)\n",
    "t1, t2 = np.meshgrid(t1s, t2s)\n",
    "T = np.c_[t1.ravel(), t2.ravel()]\n",
    "Xr = np.array([[1, 1], [1, -1], [1, 0.5]])\n",
    "yr = 2 * Xr[:, :1] + 0.5 * Xr[:, 1:]\n",
    "\n",
    "J = (1 / len(Xr) * ((T @ Xr.T - yr.T) ** 2).sum(axis=1)).reshape(t1.shape)\n",
    "\n",
    "N1 = np.linalg.norm(T, ord=1, axis=1).reshape(t1.shape)\n",
    "N2 = np.linalg.norm(T, ord=2, axis=1).reshape(t1.shape)\n",
    "\n",
    "t_min_idx = np.unravel_index(J.argmin(), J.shape)\n",
    "t1_min, t2_min = t1[t_min_idx], t2[t_min_idx]\n",
    "\n",
    "t_init = np.array([[0.25], [-1]])\n",
    "\n",
    "def bgd_path(theta, X, y, l1, l2, core=1, eta=0.05, n_iterations=200):\n",
    "    path = [theta]\n",
    "    for iteration in range(n_iterations):\n",
    "        gradients = (core * 2 / len(X) * X.T @ (X @ theta - y)\n",
    "                     + l1 * np.sign(theta) + l2 * theta)\n",
    "        theta = theta - eta * gradients\n",
    "        path.append(theta)\n",
    "    return np.array(path)\n",
    "\n",
    "fig, axes = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(10.1, 8))\n",
    "\n",
    "for i, N, l1, l2, title in ((0, N1, 2.0, 0, \"Lasso\"), (1, N2, 0, 2.0, \"Ridge\")):\n",
    "    JR = J + l1 * N1 + l2 * 0.5 * N2 ** 2\n",
    "\n",
    "    tr_min_idx = np.unravel_index(JR.argmin(), JR.shape)\n",
    "    t1r_min, t2r_min = t1[tr_min_idx], t2[tr_min_idx]\n",
    "\n",
    "    levels = np.exp(np.linspace(0, 1, 20)) - 1\n",
    "    levelsJ = levels * (J.max() - J.min()) + J.min()\n",
    "    levelsJR = levels * (JR.max() - JR.min()) + JR.min()\n",
    "    levelsN = np.linspace(0, N.max(), 10)\n",
    "\n",
    "    path_J = bgd_path(t_init, Xr, yr, l1=0, l2=0)\n",
    "    path_JR = bgd_path(t_init, Xr, yr, l1, l2)\n",
    "    path_N = bgd_path(theta=np.array([[2.0], [0.5]]), X=Xr, y=yr,\n",
    "                      l1=np.sign(l1) / 3, l2=np.sign(l2), core=0)\n",
    "    ax = axes[i, 0]\n",
    "    ax.grid()\n",
    "    ax.axhline(y=0, color=\"k\")\n",
    "    ax.axvline(x=0, color=\"k\")\n",
    "    ax.contourf(t1, t2, N / 2.0, levels=levelsN)\n",
    "    ax.plot(path_N[:, 0], path_N[:, 1], \"y--\")\n",
    "    ax.plot(0, 0, \"ys\")\n",
    "    ax.plot(t1_min, t2_min, \"ys\")\n",
    "    ax.set_title(fr\"$\\ell_{i + 1}$ penalty\")\n",
    "    ax.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        ax.set_xlabel(r\"$\\theta_1$\")\n",
    "    ax.set_ylabel(r\"$\\theta_2$\", rotation=0)\n",
    "\n",
    "    ax = axes[i, 1]\n",
    "    ax.grid()\n",
    "    ax.axhline(y=0, color=\"k\")\n",
    "    ax.axvline(x=0, color=\"k\")\n",
    "    ax.contourf(t1, t2, JR, levels=levelsJR, alpha=0.9)\n",
    "    ax.plot(path_JR[:, 0], path_JR[:, 1], \"w-o\")\n",
    "    ax.plot(path_N[:, 0], path_N[:, 1], \"y--\")\n",
    "    ax.plot(0, 0, \"ys\")\n",
    "    ax.plot(t1_min, t2_min, \"ys\")\n",
    "    ax.plot(t1r_min, t2r_min, \"rs\")\n",
    "    ax.set_title(title)\n",
    "    ax.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        ax.set_xlabel(r\"$\\theta_1$\")\n",
    "\n",
    "save_fig(\"lasso_vs_ridge_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Elastic Net"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.54333232])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import ElasticNet\n",
    "\n",
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Early Stopping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's go back to the quadratic dataset we used earlier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from copy import deepcopy\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# extra code – creates the same quadratic dataset as earlier and splits it\n",
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X ** 2 + X + 2 + np.random.randn(m, 1)\n",
    "X_train, y_train = X[: m // 2], y[: m // 2, 0]\n",
    "X_valid, y_valid = X[m // 2 :], y[m // 2 :, 0]\n",
    "\n",
    "preprocessing = make_pipeline(PolynomialFeatures(degree=90, include_bias=False),\n",
    "                              StandardScaler())\n",
    "X_train_prep = preprocessing.fit_transform(X_train)\n",
    "X_valid_prep = preprocessing.transform(X_valid)\n",
    "sgd_reg = SGDRegressor(penalty=None, eta0=0.002, random_state=42)\n",
    "n_epochs = 500\n",
    "best_valid_rmse = float('inf')\n",
    "train_errors, val_errors = [], []  # extra code – it's for the figure below\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    sgd_reg.partial_fit(X_train_prep, y_train)\n",
    "    y_valid_predict = sgd_reg.predict(X_valid_prep)\n",
    "    val_error = mean_squared_error(y_valid, y_valid_predict, squared=False)\n",
    "    if val_error < best_valid_rmse:\n",
    "        best_valid_rmse = val_error\n",
    "        best_model = deepcopy(sgd_reg)\n",
    "\n",
    "    # extra code – we evaluate the train error and save it for the figure\n",
    "    y_train_predict = sgd_reg.predict(X_train_prep)\n",
    "    train_error = mean_squared_error(y_train, y_train_predict, squared=False)\n",
    "    val_errors.append(val_error)\n",
    "    train_errors.append(train_error)\n",
    "\n",
    "# extra code – this section generates and saves Figure 4–20\n",
    "best_epoch = np.argmin(val_errors)\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.annotate('Best model',\n",
    "             xy=(best_epoch, best_valid_rmse),\n",
    "             xytext=(best_epoch, best_valid_rmse + 0.5),\n",
    "             ha=\"center\",\n",
    "             arrowprops=dict(facecolor='black', shrink=0.05))\n",
    "plt.plot([0, n_epochs], [best_valid_rmse, best_valid_rmse], \"k:\", linewidth=2)\n",
    "plt.plot(val_errors, \"b-\", linewidth=3, label=\"Validation set\")\n",
    "plt.plot(best_epoch, best_valid_rmse, \"bo\")\n",
    "plt.plot(train_errors, \"r--\", linewidth=2, label=\"Training set\")\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.xlabel(\"Epoch\")\n",
    "plt.ylabel(\"RMSE\")\n",
    "plt.axis([0, n_epochs, 0, 3.5])\n",
    "plt.grid()\n",
    "save_fig(\"early_stopping_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating Probabilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – generates and saves Figure 4–21\n",
    "\n",
    "lim = 6\n",
    "t = np.linspace(-lim, lim, 100)\n",
    "sig = 1 / (1 + np.exp(-t))\n",
    "\n",
    "plt.figure(figsize=(8, 3))\n",
    "plt.plot([-lim, lim], [0, 0], \"k-\")\n",
    "plt.plot([-lim, lim], [0.5, 0.5], \"k:\")\n",
    "plt.plot([-lim, lim], [1, 1], \"k:\")\n",
    "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n",
    "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\dfrac{1}{1 + e^{-t}}$\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.axis([-lim, lim, -0.1, 1.1])\n",
    "plt.gca().set_yticks([0, 0.25, 0.5, 0.75, 1])\n",
    "plt.grid()\n",
    "save_fig(\"logistic_function_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decision Boundaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data',\n",
       " 'target',\n",
       " 'frame',\n",
       " 'target_names',\n",
       " 'DESCR',\n",
       " 'feature_names',\n",
       " 'filename',\n",
       " 'data_module']"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "\n",
    "iris = load_iris(as_frame=True)\n",
    "list(iris)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "                \n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n"
     ]
    }
   ],
   "source": [
    "print(iris.DESCR)  # extra code – it's a bit too long"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
       "0                5.1               3.5                1.4               0.2\n",
       "1                4.9               3.0                1.4               0.2\n",
       "2                4.7               3.2                1.3               0.2"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.data.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0\n",
       "1    0\n",
       "2    0\n",
       "Name: target, dtype: int64"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.target.head(3)  # note that the instances are not shuffled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['setosa', 'versicolor', 'virginica'], dtype='<U10')"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.target_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(random_state=42)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X = iris.data[[\"petal width (cm)\"]].values\n",
    "y = iris.target_names[iris.target] == 'virginica'\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
    "\n",
    "log_reg = LogisticRegression(random_state=42)\n",
    "log_reg.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)  # reshape to get a column vector\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "decision_boundary = X_new[y_proba[:, 1] >= 0.5][0, 0]\n",
    "\n",
    "plt.figure(figsize=(8, 3))  # extra code – not needed, just formatting\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2,\n",
    "         label=\"Not Iris virginica proba\")\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris virginica proba\")\n",
    "plt.plot([decision_boundary, decision_boundary], [0, 1], \"k:\", linewidth=2,\n",
    "         label=\"Decision boundary\")\n",
    "\n",
    "# extra code – this section beautifies and saves Figure 4–23\n",
    "plt.arrow(x=decision_boundary, y=0.08, dx=-0.3, dy=0,\n",
    "          head_width=0.05, head_length=0.1, fc=\"b\", ec=\"b\")\n",
    "plt.arrow(x=decision_boundary, y=0.92, dx=0.3, dy=0,\n",
    "          head_width=0.05, head_length=0.1, fc=\"g\", ec=\"g\")\n",
    "plt.plot(X_train[y_train == 0], y_train[y_train == 0], \"bs\")\n",
    "plt.plot(X_train[y_train == 1], y_train[y_train == 1], \"g^\")\n",
    "plt.xlabel(\"Petal width (cm)\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.legend(loc=\"center left\")\n",
    "plt.axis([0, 3, -0.02, 1.02])\n",
    "plt.grid()\n",
    "save_fig(\"logistic_regression_plot\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6516516516516517"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decision_boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–24\n",
    "\n",
    "X = iris.data[[\"petal length (cm)\", \"petal width (cm)\"]].values\n",
    "y = iris.target_names[iris.target] == 'virginica'\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
    "\n",
    "log_reg = LogisticRegression(C=2, random_state=42)\n",
    "log_reg.fit(X_train, y_train)\n",
    "\n",
    "# for the contour plot\n",
    "x0, x1 = np.meshgrid(np.linspace(2.9, 7, 500).reshape(-1, 1),\n",
    "                     np.linspace(0.8, 2.7, 200).reshape(-1, 1))\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]  # one instance per point on the figure\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "zz = y_proba[:, 1].reshape(x0.shape)\n",
    "\n",
    "# for the decision boundary\n",
    "left_right = np.array([2.9, 7])\n",
    "boundary = -((log_reg.coef_[0, 0] * left_right + log_reg.intercept_[0])\n",
    "             / log_reg.coef_[0, 1])\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X_train[y_train == 0, 0], X_train[y_train == 0, 1], \"bs\")\n",
    "plt.plot(X_train[y_train == 1, 0], X_train[y_train == 1, 1], \"g^\")\n",
    "contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1)\n",
    "plt.plot(left_right, boundary, \"k--\", linewidth=3)\n",
    "plt.text(3.5, 1.27, \"Not Iris virginica\", color=\"b\", ha=\"center\")\n",
    "plt.text(6.5, 2.3, \"Iris virginica\", color=\"g\", ha=\"center\")\n",
    "plt.xlabel(\"Petal length\")\n",
    "plt.ylabel(\"Petal width\")\n",
    "plt.axis([2.9, 7, 0.8, 2.7])\n",
    "plt.grid()\n",
    "save_fig(\"logistic_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Softmax Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=30, random_state=42)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = iris.data[[\"petal length (cm)\", \"petal width (cm)\"]].values\n",
    "y = iris[\"target\"]\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
    "\n",
    "softmax_reg = LogisticRegression(C=30, random_state=42)\n",
    "softmax_reg.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict([[5, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.  , 0.04, 0.96]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict_proba([[5, 2]]).round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–25\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "custom_cmap = ListedColormap([\"#fafab0\", \"#9898ff\", \"#a0faa0\"])\n",
    "\n",
    "x0, x1 = np.meshgrid(np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "                     np.linspace(0, 3.5, 200).reshape(-1, 1))\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "y_proba = softmax_reg.predict_proba(X_new)\n",
    "y_predict = softmax_reg.predict(X_new)\n",
    "\n",
    "zz1 = y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y == 2, 0], X[y == 2, 1], \"g^\", label=\"Iris virginica\")\n",
    "plt.plot(X[y == 1, 0], X[y == 1, 1], \"bs\", label=\"Iris versicolor\")\n",
    "plt.plot(X[y == 0, 0], X[y == 0, 1], \"yo\", label=\"Iris setosa\")\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=\"hot\")\n",
    "plt.clabel(contour, inline=1)\n",
    "plt.xlabel(\"Petal length\")\n",
    "plt.ylabel(\"Petal width\")\n",
    "plt.legend(loc=\"center left\")\n",
    "plt.axis([0.5, 7, 0, 3.5])\n",
    "plt.grid()\n",
    "save_fig(\"softmax_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. to 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. If you have a training set with millions of features you can use Stochastic Gradient Descent or Mini-batch Gradient Descent, and perhaps Batch Gradient Descent if the training set fits in memory. But you cannot use the Normal Equation or the SVD approach because the computational complexity grows quickly (more than quadratically) with the number of features.\n",
    "2. If the features in your training set have very different scales, the cost function will have the shape of an elongated bowl, so the Gradient Descent algorithms will take a long time to converge. To solve this you should scale the data before training the model. Note that the Normal Equation or SVD approach will work just fine without scaling. Moreover, regularized models may converge to a suboptimal solution if the features are not scaled: since regularization penalizes large weights, features with smaller values will tend to be ignored compared to features with larger values.\n",
    "3. Gradient Descent cannot get stuck in a local minimum when training a Logistic Regression model because the cost function is convex. _Convex_ means that if you draw a straight line between any two points on the curve, the line never crosses the curve.\n",
    "4. If the optimization problem is convex (such as Linear Regression or Logistic Regression), and assuming the learning rate is not too high, then all Gradient Descent algorithms will approach the global optimum and end up producing fairly similar models. However, unless you gradually reduce the learning rate, Stochastic GD and Mini-batch GD will never truly converge; instead, they will keep jumping back and forth around the global optimum. This means that even if you let them run for a very long time, these Gradient Descent algorithms will produce slightly different models.\n",
    "5. If the validation error consistently goes up after every epoch, then one possibility is that the learning rate is too high and the algorithm is diverging. If the training error also goes up, then this is clearly the problem and you should reduce the learning rate. However, if the training error is not going up, then your model is overfitting the training set and you should stop training.\n",
    "6. Due to their random nature, neither Stochastic Gradient Descent nor Mini-batch Gradient Descent is guaranteed to make progress at every single training iteration. So if you immediately stop training when the validation error goes up, you may stop much too early, before the optimum is reached. A better option is to save the model at regular intervals; then, when it has not improved for a long time (meaning it will probably never beat the record), you can revert to the best saved model.\n",
    "7. Stochastic Gradient Descent has the fastest training iteration since it considers only one training instance at a time, so it is generally the first to reach the vicinity of the global optimum (or Mini-batch GD with a very small mini-batch size). However, only Batch Gradient Descent will actually converge, given enough training time. As mentioned, Stochastic GD and Mini-batch GD will bounce around the optimum, unless you gradually reduce the learning rate.\n",
    "8. If the validation error is much higher than the training error, this is likely because your model is overfitting the training set. One way to try to fix this is to reduce the polynomial degree: a model with fewer degrees of freedom is less likely to overfit. Another thing you can try is to regularize the model—for example, by adding an ℓ₂ penalty (Ridge) or an ℓ₁ penalty (Lasso) to the cost function. This will also reduce the degrees of freedom of the model. Lastly, you can try to increase the size of the training set.\n",
    "9. If both the training error and the validation error are almost equal and fairly high, the model is likely underfitting the training set, which means it has a high bias. You should try reducing the regularization hyperparameter _α_.\n",
    "10. Let's see:\n",
    "  * A model with some regularization typically performs better than a model without any regularization, so you should generally prefer Ridge Regression over plain Linear Regression.\n",
    "  * Lasso Regression uses an ℓ₁ penalty, which tends to push the weights down to exactly zero. This leads to sparse models, where all weights are zero except for the most important weights. This is a way to perform feature selection automatically, which is good if you suspect that only a few features actually matter. When you are not sure, you should prefer Ridge Regression.\n",
    "  * Elastic Net is generally preferred over Lasso since Lasso may behave erratically in some cases (when several features are strongly correlated or when there are more features than training instances). However, it does add an extra hyperparameter to tune. If you want Lasso without the erratic behavior, you can just use Elastic Net with an `l1_ratio` close to 1.\n",
    "11. If you want to classify pictures as outdoor/indoor and daytime/nighttime, since these are not exclusive classes (i.e., all four combinations are possible) you should train two Logistic Regression classifiers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12. Batch Gradient Descent with early stopping for Softmax Regression\n",
    "Exercise: _Implement Batch Gradient Descent with early stopping for Softmax Regression without using Scikit-Learn, only NumPy. Use it on a classification task such as the iris dataset._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by loading the data. We will just reuse the Iris dataset we loaded earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris.data[[\"petal length (cm)\", \"petal width (cm)\"]].values\n",
    "y = iris[\"target\"].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to add the bias term for every instance ($x_0 = 1$). The easiest option to do this would be to use Scikit-Learn's `add_dummy_feature()` function, but the point of this exercise is to get a better understanding of the algorithms by implementing them manually. So here is one possible implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_with_bias = np.c_[np.ones(len(X)), X]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The easiest option to split the dataset into a training set, a validation set and a test set would be to use Scikit-Learn's `train_test_split()` function, but again, we want to do it manually:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_ratio = 0.2\n",
    "validation_ratio = 0.2\n",
    "total_size = len(X_with_bias)\n",
    "\n",
    "test_size = int(total_size * test_ratio)\n",
    "validation_size = int(total_size * validation_ratio)\n",
    "train_size = total_size - test_size - validation_size\n",
    "\n",
    "np.random.seed(42)\n",
    "rnd_indices = np.random.permutation(total_size)\n",
    "\n",
    "X_train = X_with_bias[rnd_indices[:train_size]]\n",
    "y_train = y[rnd_indices[:train_size]]\n",
    "X_valid = X_with_bias[rnd_indices[train_size:-test_size]]\n",
    "y_valid = y[rnd_indices[train_size:-test_size]]\n",
    "X_test = X_with_bias[rnd_indices[-test_size:]]\n",
    "y_test = y[rnd_indices[-test_size:]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The targets are currently class indices (0, 1 or 2), but we need target class probabilities to train the Softmax Regression model. Each instance will have target class probabilities equal to 0.0 for all classes except for the target class which will have a probability of 1.0 (in other words, the vector of class probabilities for any given instance is a one-hot vector). Let's write a small function to convert the vector of class indices into a matrix containing a one-hot vector for each instance. To understand this code, you need to know that `np.diag(np.ones(n))` creates an n×n matrix full of 0s except for 1s on the main diagonal. Moreover, if `a` is a NumPy array, then `a[[1, 3, 2]]` returns an array with 3 rows equal to `a[1]`, `a[3]` and `a[2]` (this is [advanced NumPy indexing](https://numpy.org/doc/stable/user/basics.indexing.html#advanced-indexing))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "def to_one_hot(y):\n",
    "    return np.diag(np.ones(y.max() + 1))[y]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test this function on the first 10 instances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 2, 1, 1, 0, 1, 2, 1, 1])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 0.],\n",
       "       [1., 0., 0.],\n",
       "       [0., 0., 1.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_one_hot(y_train[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks good, so let's create the target class probabilities matrix for the training set and the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_train_one_hot = to_one_hot(y_train)\n",
    "Y_valid_one_hot = to_one_hot(y_valid)\n",
    "Y_test_one_hot = to_one_hot(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's scale the inputs. We compute the mean and standard deviation of each feature on the training set (except for the bias feature), then we center and scale each feature in the training set, the validation set, and the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean = X_train[:, 1:].mean(axis=0)\n",
    "std = X_train[:, 1:].std(axis=0)\n",
    "X_train[:, 1:] = (X_train[:, 1:] - mean) / std\n",
    "X_valid[:, 1:] = (X_valid[:, 1:] - mean) / std\n",
    "X_test[:, 1:] = (X_test[:, 1:] - mean) / std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's implement the Softmax function. Recall that it is defined by the following equation:\n",
    "\n",
    "$\\sigma\\left(\\mathbf{s}(\\mathbf{x})\\right)_k = \\dfrac{\\exp\\left(s_k(\\mathbf{x})\\right)}{\\sum\\limits_{j=1}^{K}{\\exp\\left(s_j(\\mathbf{x})\\right)}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax(logits):\n",
    "    exps = np.exp(logits)\n",
    "    exp_sums = exps.sum(axis=1, keepdims=True)\n",
    "    return exps / exp_sums"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are almost ready to start training. Let's define the number of inputs and outputs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_inputs = X_train.shape[1]  # == 3 (2 features plus the bias term)\n",
    "n_outputs = len(np.unique(y_train))  # == 3 (there are 3 iris classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now here comes the hardest part: training! Theoretically, it's simple: it's just a matter of translating the math equations into Python code. But in practice, it can be quite tricky: in particular, it's easy to mix up the order of the terms, or the indices. You can even end up with code that looks like it's working but is actually not computing exactly the right thing. When unsure, you should write down the shape of each term in the equation and make sure the corresponding terms in your code match closely. It can also help to evaluate each term independently and print them out. The good news it that you won't have to do this everyday, since all this is well implemented by Scikit-Learn, but it will help you understand what's going on under the hood.\n",
    "\n",
    "So the equations we will need are the cost function:\n",
    "\n",
    "$J(\\mathbf{\\Theta}) =\n",
    "- \\dfrac{1}{m}\\sum\\limits_{i=1}^{m}\\sum\\limits_{k=1}^{K}{y_k^{(i)}\\log\\left(\\hat{p}_k^{(i)}\\right)}$\n",
    "\n",
    "And the equation for the gradients:\n",
    "\n",
    "$\\nabla_{\\mathbf{\\theta}^{(k)}} \\, J(\\mathbf{\\Theta}) = \\dfrac{1}{m} \\sum\\limits_{i=1}^{m}{ \\left ( \\hat{p}^{(i)}_k - y_k^{(i)} \\right ) \\mathbf{x}^{(i)}}$\n",
    "\n",
    "Note that $\\log\\left(\\hat{p}_k^{(i)}\\right)$ may not be computable if $\\hat{p}_k^{(i)} = 0$. So we will add a tiny value $\\epsilon$ to $\\log\\left(\\hat{p}_k^{(i)}\\right)$ to avoid getting `nan` values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 3.7085808486476917\n",
      "1000 0.14519367480830644\n",
      "2000 0.1301309575504088\n",
      "3000 0.12009639326384539\n",
      "4000 0.11372961364786884\n",
      "5000 0.11002459532472425\n"
     ]
    }
   ],
   "source": [
    "eta = 0.5\n",
    "n_epochs = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-5\n",
    "\n",
    "np.random.seed(42)\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    logits = X_train @ Theta\n",
    "    Y_proba = softmax(logits)\n",
    "    if epoch % 1000 == 0:\n",
    "        Y_proba_valid = softmax(X_valid @ Theta)\n",
    "        xentropy_losses = -(Y_valid_one_hot * np.log(Y_proba_valid + epsilon))\n",
    "        print(epoch, xentropy_losses.sum(axis=1).mean())\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    gradients = 1 / m * X_train.T @ error\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And that's it! The Softmax model is trained. Let's look at the model parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.41931626,  6.11112089, -5.52429876],\n",
       "       [-6.53054533, -0.74608616,  8.33137102],\n",
       "       [-5.28115784,  0.25152675,  6.90680425]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make predictions for the validation set and check the accuracy score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid @ Theta\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = Y_proba.argmax(axis=1)\n",
    "\n",
    "accuracy_score = (y_predict == y_valid).mean()\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, this model looks pretty ok. For the sake of the exercise, let's add a bit of $\\ell_2$ regularization. The following training code is similar to the one above, but the loss now has an additional $\\ell_2$ penalty, and the gradients have the proper additional term (note that we don't regularize the first element of `Theta` since this corresponds to the bias term). Also, let's try increasing the learning rate `eta`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 3.7372\n",
      "1000 0.3259\n",
      "2000 0.3259\n",
      "3000 0.3259\n",
      "4000 0.3259\n",
      "5000 0.3259\n"
     ]
    }
   ],
   "source": [
    "eta = 0.5\n",
    "n_epochs = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-5\n",
    "alpha = 0.01  # regularization hyperparameter\n",
    "\n",
    "np.random.seed(42)\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    logits = X_train @ Theta\n",
    "    Y_proba = softmax(logits)\n",
    "    if epoch % 1000 == 0:\n",
    "        Y_proba_valid = softmax(X_valid @ Theta)\n",
    "        xentropy_losses = -(Y_valid_one_hot * np.log(Y_proba_valid + epsilon))\n",
    "        l2_loss = 1 / 2 * (Theta[1:] ** 2).sum()\n",
    "        total_loss = xentropy_losses.sum(axis=1).mean() + alpha * l2_loss\n",
    "        print(epoch, total_loss.round(4))\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    gradients = 1 / m * X_train.T @ error\n",
    "    gradients += np.r_[np.zeros([1, n_outputs]), alpha * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of the additional $\\ell_2$ penalty, the loss seems greater than earlier, but perhaps this model will perform better? Let's find out:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid @ Theta\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = Y_proba.argmax(axis=1)\n",
    "\n",
    "accuracy_score = (y_predict == y_valid).mean()\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, the $\\ell_2$ penalty did not change the test accuracy. Perhaps try fine-tuning `alpha`?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's add early stopping. For this we just need to measure the loss on the validation set at every iteration and stop when the error starts growing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 3.7372\n",
      "281 0.3256\n",
      "282 0.3256 early stopping!\n"
     ]
    }
   ],
   "source": [
    "eta = 0.5\n",
    "n_epochs = 50_001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-5\n",
    "C = 100  # regularization hyperparameter\n",
    "best_loss = np.infty\n",
    "\n",
    "np.random.seed(42)\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    logits = X_train @ Theta\n",
    "    Y_proba = softmax(logits)\n",
    "    Y_proba_valid = softmax(X_valid @ Theta)\n",
    "    xentropy_losses = -(Y_valid_one_hot * np.log(Y_proba_valid + epsilon))\n",
    "    l2_loss = 1 / 2 * (Theta[1:] ** 2).sum()\n",
    "    total_loss = xentropy_losses.sum(axis=1).mean() + 1 / C * l2_loss\n",
    "    if epoch % 1000 == 0:\n",
    "        print(epoch, total_loss.round(4))\n",
    "    if total_loss < best_loss:\n",
    "        best_loss = total_loss\n",
    "    else:\n",
    "        print(epoch - 1, best_loss.round(4))\n",
    "        print(epoch, total_loss.round(4), \"early stopping!\")\n",
    "        break\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    gradients = 1 / m * X_train.T @ error\n",
    "    gradients += np.r_[np.zeros([1, n_outputs]), 1 / C * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid @ Theta\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = Y_proba.argmax(axis=1)\n",
    "\n",
    "accuracy_score = (y_predict == y_valid).mean()\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oh well, still no change in validation accuracy, but at least early stopping shortened training a bit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot the model's predictions on the whole dataset (remember to scale all features fed to the model):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "custom_cmap = mpl.colors.ListedColormap(['#fafab0', '#9898ff', '#a0faa0'])\n",
    "\n",
    "x0, x1 = np.meshgrid(np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "                     np.linspace(0, 3.5, 200).reshape(-1, 1))\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "X_new = (X_new - mean) / std\n",
    "X_new_with_bias = np.c_[np.ones(len(X_new)), X_new]\n",
    "\n",
    "logits = X_new_with_bias @ Theta\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = Y_proba.argmax(axis=1)\n",
    "\n",
    "zz1 = Y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y == 2, 0], X[y == 2, 1], \"g^\", label=\"Iris virginica\")\n",
    "plt.plot(X[y == 1, 0], X[y == 1, 1], \"bs\", label=\"Iris versicolor\")\n",
    "plt.plot(X[y == 0, 0], X[y == 0, 1], \"yo\", label=\"Iris setosa\")\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=\"hot\")\n",
    "plt.clabel(contour, inline=1)\n",
    "plt.xlabel(\"Petal length\")\n",
    "plt.ylabel(\"Petal width\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now let's measure the final model's accuracy on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9666666666666667"
      ]
     },
     "execution_count": 80,
     "metadata": {},
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    }
   ],
   "source": [
    "logits = X_test @ Theta\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = Y_proba.argmax(axis=1)\n",
    "\n",
    "accuracy_score = (y_predict == y_test).mean()\n",
    "accuracy_score"
   ]
  },
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    "Well we get even better performance on the test set. This variability is likely due to the very small size of the dataset: depending on how you sample the training set, validation set and the test set, you can get quite different results. Try changing the random seed and running the code again a few times, you will see that the results will vary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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